A trust has always at least one trustee. There are, however, many types of trustees. A sole trustee is someone who carries out the terms of your trust alone. Two individuals carrying out the terms of your trust together are called co-trustees. The co-trustees may have to work together, something for you to keep in mind since you want to choose people who can work well together.
An alternate co-trustee is someone that replaces one of the co-trustees in case they cannot or will not serve. This is not to be confused with a successor trustee. A sole successor trustee functions as the second point of original reference after the trustees. They are called to serve the terms of the trust if the trustee(s) cannot or will not serve. You can also appoint two people here instead of one. These are called successor co-trustees. If any of these two cannot or will not serve, you can appoint an alternate successor co-trustee.
Finally, there are also corporate trustees. Such trustees are usually a bank or a company that specializes in trust management.
See also: Bond, Fiduciary, Natural Person